## PRP Records

### Probable Primes Top 10000

#### (295756 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 9751 2^331110+1870459 99675 Enzo Doria 05/2016 9752 5*2^331075+7 99665 Lelio R Paula 08/2014 9753 25776^7351+7351^25776 99659 Hans Havermann 02/2018 9754 (16*10^99656-31)/3 99657 Robert Price 03/2016 9755 (6059^26347-1)/6058 99652 Serge Batalov 06/2022 9756 (15544^23773-1)/15543 99642 Serge Batalov 06/2022 9758 2^330968+345 99632 Lelio R Paula 09/2016 9757 (2^330969+690)/2 99632 Stefano Morozzi 09/2020 9760 2*5^142528-7 99624 Lelio R Paula 11/2014 9759 2^330942+77329 99624 Enzo Doria 05/2016 9761 14^86914-99 99615 Lelio R Paula 08/2016 9762 (19*2^330902+1)/77 99611 Lelio R Paula 11/2013 9763 22971^21692+21692^22971 99610 Hans Havermann 03/2018 9764 2^330845+71687 99595 Enzo Doria 04/2016 9765 (26667^22501-1)/26666 99585 Serge Batalov 06/2022 9766 (23*2^330770+1)/3 99573 Lelio R Paula 11/2013 9767 24494^11613+11613^24494 99567 Hans Havermann 03/2018 9768 2^330735+8415 99562 Lelio R Paula 09/2016 9769 2^330720+74071 99557 Enzo Doria 04/2016 9770 (10405^24781-1)/10404 99548 Serge Batalov 06/2022 9772 31^66738-2 99531 Lelio R Paula 09/2013 9771 (9002^25171-1)/9001 99531 Serge Batalov 06/2022 9773 (5023^26893-1)/5022 99527 Serge Batalov 06/2022 9774 7*3^208567+4 99513 Lelio R Paula 08/2014 9775 (15881^23689-1)/15880 99511 Serge Batalov 06/2022 9776 (13*10^99508+47)/3 99509 Robert Price 01/2017 9777 2^330553+779 99507 Lelio R Paula 01/2013 9778 15^84606-94 99505 Lelio R Paula 08/2016 9779 (10^99497+173)/3 99497 Robert Price 05/2021 9780 9*10^99493-43 99494 Robert Price 09/2021 9781 6^127858+47 99493 Lelio R Paula 08/2016 9782 5^142337+48 99490 Lelio R Paula 08/2016 9783 7^117724-20 99489 Lelio R Paula 08/2016 9784 (559^36209-1)/558 99479 Serge Batalov 06/2022 9785 (13470^24091-1)/13469 99477 Serge Batalov 06/2022 9786 (29*10^99474-17)/3 99475 Erik Branger 09/2014 9787 (185*10^99466-11)/3 99468 Robert Price 10/2020 9788 (2^330410+2038)/2 99464 Stefano Morozzi 09/2020 9789 (9*2^330407-1)/7 99463 Lelio R Paula 03/2014 9790 (516*32^66077-175)/31 99458 Eric Chen 04/2023 9791 (2863^28771-1)/2862 99453 Serge Batalov 06/2022 9792 (2^330373+2114)/2 99452 Stefano Morozzi 09/2020 9793 179^44142-44142^179 99446 Norman Luhn 08/2024 9794 (68*10^99441+7)/3 99443 Robert Price 03/2016 9795 10^99434+155571 99435 Patrick De Geest 04/2020 9796 10^99434-123456789 99434 Robert Price 02/2020 9797 10^99434-191237 99434 Patrick De Geest 04/2020 9798 46^59791-45^59791 99418 Jean-Louis Charton 01/2013 9799 23839^14802+14802^23839 99417 Hans Havermann 02/2018 9800 (2*10^99408+529)/9 99408 Robert Price 01/2017 9801 (2^330216+3510)/2 99405 Stefano Morozzi 09/2020 9802 53^57646-2 99398 Lelio R Paula 09/2013 9803 2^330165+1870025 99390 Enzo Doria 05/2016 9804 7*10^99383+97 99384 Robert Price 09/2021 9805 2^330142-155 99383 Lelio R Paula 12/2012 9806 2^330088-115259 99367 Enzo Doria 06/2015 9807 24216^12671+12671^24216 99354 Hans Havermann 01/2018 9808 Phi(200548,10)/3208769 99354 Makoto Kamada 04/2019 9809 (746*10^99303+1)/9 99305 Robert Price 02/2017 9810 3^208107+40 99293 Lelio R Paula 08/2016 9811 2^329843+211343 99293 Enzo Doria 08/2023 9812 (3939^27617-1)/3938 99291 Serge Batalov 06/2022 9813 (5*2^329833-1)/369 99288 Lelio R Paula 02/2014 9814 8*3^208093+5 99287 Lelio R Paula 08/2014 9815 5^142043+56 99284 Lelio R Paula 08/2016 9816 (13*10^99282-157)/9 99283 Robert Price 05/2021 9817 (10^99284+7)/53/67 99281 Alfred Reich 06/2021 9818 22*10^99275+7 99277 Robert Price 04/2016 9819 2^329778+1876189 99274 Enzo Doria 07/2016 9820 (149557^19321-1)/(149557^139-1) 99264 Ryan Propper 11/2023 9821 (6580^25997-1)/6579 99259 Serge Batalov 06/2022 9822 (2249^29611-1)/2248 99253 Serge Batalov 06/2022 9823 (10^99239-13)/3 99239 Robert Price 02/2017 9824 (1199^32233-1)/1198 99237 Serge Batalov 06/2022 9826 3^207987+62 99236 Lelio R Paula 08/2016 9825 (62*10^99235+91)/9 99236 Robert Price 07/2021 9827 2^329638+49 99231 Lelio R Paula 12/2012 9828 7^117413-18 99226 Lelio R Paula 08/2016 9829 2^329586-458903 99216 Enzo Doria 04/2015 9830 (6290^26119-1)/6289 99214 Serge Batalov 06/2022 9832 2^329553+101 99206 Lelio R Paula 12/2012 9831 (21297^22921-1)/21296 99206 Serge Batalov 06/2022 9833 2^329551-112897 99205 Enzo Doria 06/2014 9834 (3^207925+7)/50 99204 Lelio R Paula 09/2013 9835 U(477331)/57279721 99202 Serge Batalov 07/2024 9836 6^127458-17993 99182 Enzo Doria 03/2013 9837 27197^4428+4428^27197 99166 Hans Havermann 10/2017 9838 (46*10^99143-1)/9 99144 Robert Price 12/2014 9839 (64*10^99135+161)/9 99136 Robert Price 08/2022 9840 7*10^99133+69 99134 Robert Price 10/2017 9841 (21701^22861-1)/21700 99132 Serge Batalov 06/2022 9842 18^78968-3065 99127 Enzo Doria 03/2013 9843 25927^6654+6654^25927 99122 Hans Havermann 10/2017 9844 87915!4+16 99122 Robert Price 09/2019 9845 2^329259+189 99117 Lelio R Paula 12/2012 9846 8*10^99113+39 99114 Robert Price 01/2017 9847 6^127364+77 99109 Lelio R Paula 08/2016 9848 (82*10^99103+143)/9 99104 Robert Price 06/2021 9849 (11414^24421-1)/11413 99083 Serge Batalov 06/2022 9850 (2^329135+1110)/2 99080 Stefano Morozzi 09/2020 9851 (22089^22807-1)/22088 99074 Serge Batalov 06/2022 9852 (59*10^99069+391)/9 99070 Robert Price 03/2021 9853 (797*10^99061-41)/9 99063 Robert Price 04/2022 9854 2^329058-287681 99057 Harrison Mesh 06/2022 9855 6^127285+13 99047 Lelio R Paula 08/2016 9856 (228581#+235862)/(2^3*11*71*151) 99044 Makoto Morimoto 10/2017 9857 2^329007+73283 99041 Enzo Doria 04/2016 9858 (145413^19321-1)/(145413^139-1) 99030 Ryan Propper 11/2023 9859 5*3^207543-8 99024 Lelio R Paula 08/2014 9860 (2^328930+570)/2 99018 Stefano Morozzi 09/2020 9861 2^328885+149 99005 Lelio R Paula 12/2012 9862 23392^17075+17075^23392 99004 Hans Havermann 09/2017 9863 (7424^25579-1)/7423 99004 Serge Batalov 06/2022 9864 (2^328879-9)/119 99001 Lelio R Paula 10/2013 9865 140^46129-46129^140 98999 Norman Luhn 08/2024 9866 169^44432-44432^169 98990 Norman Luhn 08/2024 9867 5^141618+54 98987 Lelio R Paula 08/2016 9868 2^328824+24391 98986 Enzo Doria 10/2023 9869 8*10^98982+51 98983 Robert Price 05/2017 9870 (21*2^328809-1)/7709 98979 Lelio R Paula 03/2014 9871 2^328794-2797601 98977 Enzo Doria 04/2016 9872 (88331^20011-1)/88330 98972 Serge Batalov 06/2022 9873 6^127176+5 98963 Lelio R Paula 11/2014 9874 2*10^98961-21 98962 Robert Price 09/2020 9875 24262^11989+11989^24262 98960 Hans Havermann 09/2017 9876 (60138^20707-1)/60137 98958 Serge Batalov 06/2022 9877 2^328700-109709 98949 Enzo Doria 04/2014 9878 (2^328698+1810)/2 98948 Stefano Morozzi 01/2021 9879 (1014^32917-1)/1013 98947 Serge Batalov 06/2022 9880 87771!4-128 98944 Robert Price 11/2019 9881 (4576^27031-1)/4575 98943 Serge Batalov 06/2022 9882 (2^328658+3042)/2 98936 Stefano Morozzi 09/2020 9883 (1933^30103-1)/1932 98923 Serge Batalov 06/2022 9884 46711!2-2^46711 98916 Robert Price 09/2015 9885 9*7^117037+4 98909 Lelio R Paula 11/2014 9886 127^47012+126 98905 Norbert Schneider 01/2019 9887 (93826^19891-1)/93825 98900 Serge Batalov 06/2022 9889 (2^328525+1250)/2 98896 Stefano Morozzi 09/2020 9888 2^328524+625 98896 Henri Lifchitz 09/2024 9890 (10^98890+149)/3 98890 Serge Batalov 12/2014 9891 22775^21978+21978^22775 98889 Hans Havermann 08/2017 9892 2^328497-216933 98888 Enzo Doria 05/2014 9893 2^328487+32769 98885 Lelio R Paula 08/2016 9894 3^207250-112358 98884 Enzo Doria 06/2014 9895 13^88754-90 98867 Lelio R Paula 08/2016 9896 2^328406+709 98861 Lelio R Paula 02/2013 9897 2*10^98860-21 98861 Robert Price 09/2020 9898 (17*2^328413-1)/16173 98860 Lelio R Paula 03/2014 9899 7^116976+76 98857 Lelio R Paula 08/2016 9900 (2^328378+2710)/2 98852 Stefano Morozzi 09/2020 9901 (25411^22441-1)/25410 98849 Serge Batalov 06/2022 9902 (18668^23143-1)/18667 98842 Serge Batalov 06/2022 9904 2^328335+1155 98839 Lelio R Paula 08/2016 9903 2^328333-349003 98839 Harrison Mesh 06/2022 9906 (3*2^328311+1)/5 98832 Lelio R Paula 11/2013 9905 287^40210+40210^287 98832 Norbert Schneider 11/2014 9907 (2^328284+9)/1325 98821 Lelio R Paula 10/2013 9908 (21*2^328258+1)/2125 98814 Lelio R Paula 11/2013 9909 (28623^22171-1)/28622 98806 Serge Batalov 06/2022 9910 24746^9825+9825^24746 98795 Hans Havermann 07/2020 9911 26620^5143+5143^26620 98793 Hans Havermann 07/2020 9912 65^54491+48 98788 Lelio R Paula 04/2016 9913 3^207042+98 98785 Lelio R Paula 08/2016 9914 (2^328121+3110)/2 98774 Stefano Morozzi 09/2020 9915 10^98754+73383 98755 Patrick De Geest 02/2021 9918 3^206977-112756 98754 Enzo Doria 07/2014 9917 10^98754-40000000001 98754 Robert Price 09/2020 9916 10^98754-169343 98754 Patrick De Geest 02/2021 9919 7^116846-50 98747 Lelio R Paula 08/2016 9920 (19152^23059-1)/19151 98740 Serge Batalov 06/2022 9921 23267^17512+17512^23267 98730 Hans Havermann 04/2020 9922 2^327967-28635 98728 Lelio R Paula 08/2016 9923 707^34642+34642^707 98710 Norbert Schneider 12/2017 9924 (10771^24481-1)/10770 98710 Serge Batalov 06/2022 9925 6^126850-47 98709 Lelio R Paula 08/2016 9926 (2^327886+2170)/2 98704 Stefano Morozzi 09/2020 9927 (22*10^98697+47)/3 98698 Robert Price 06/2021 9928 (139706^19321-1)/(139706^139-1) 98696 Ryan Propper 11/2023 9929 8*6^126830-7 98694 Lelio R Paula 11/2014 9930 11^94770-270 98693 Enzo Doria 08/2012 9931 (2^327846+3250)/2 98692 Stefano Morozzi 01/2021 9932 2^327832+43 98688 Lelio R Paula 12/2012 9933 2^327795+761 98677 Lelio R Paula 02/2013 9934 (2^327796+1522)/2 98677 Stefano Morozzi 09/2020 9935 10^98669+147411 98670 Patrick De Geest 11/2016 9937 10^98669-9^(98669-1) 98669 Robert Price 05/2016 9936 10^98669-105249 98669 Patrick De Geest 11/2016 9938 (7911^25309-1)/7910 98657 Serge Batalov 06/2022 9939 2^327671-109801 98639 Enzo Doria 04/2014 9940 24398^11037+11037^24398 98638 Hans Havermann 10/2019 9941 5^141090-14 98618 Lelio R Paula 08/2016 9942 20^75799+47 98617 Lelio R Paula 08/2016 9943 (5452^26393-1)/5451 98616 Serge Batalov 06/2022 9944 28101^3226+3226^28101 98597 Hans Havermann 07/2020 9945 2^327515-1017 98592 Lelio R Paula 08/2016 9946 6^126692+97681 98586 Mike Oakes 04/2011 9947 2^327467-741 98578 Lelio R Paula 08/2016 9948 (2947^28411-1)/2946 98566 Serge Batalov 06/2022 9949 22713^21800+21800^22713 98540 Hans Havermann 05/2020 9950 (2^327329+9)/19 98535 Lelio R Paula 10/2013 9951 7^116577-66 98519 Lelio R Paula 08/2016 9952 (3*2^327250+1)/7 98512 Lelio R Paula 11/2013 9953 23220^17479+17479^23220 98512 Hans Havermann 03/2020 9954 (2^327240+3798)/2 98509 Stefano Morozzi 02/2021 9955 (28514^22111-1)/28513 98502 Serge Batalov 06/2022 9956 (19*2^327192+1)/275 98494 Lelio R Paula 11/2013 9957 2^327162-66945 98486 Lelio R Paula 08/2016 9958 30139^1852+1852^30139 98484 Hans Havermann 02/2020 9959 23182^17703+17703^23182 98479 Hans Havermann 01/2020 9960 4*10^98472-3 98473 Erik Branger 11/2013 9961 26167^5794+5794^26167 98466 Hans Havermann 01/2020 9962 (6883*2^327047-1)/77 98453 Lelio R Paula 05/2015 9963 (71*10^98446+1)/9 98447 Serge Batalov 11/2010 9964 (2009^29803-1)/2008 98436 Serge Batalov 06/2022 9965 13^88363+94 98432 Lelio R Paula 08/2016 9966 48^58543-47^58543 98425 Jean-Louis Charton 11/2005 9967 6^126481+41 98422 Lelio R Paula 08/2016 9968 78*10^98413-7 98415 Robert Price 05/2017 9969 22634^22263+22263^22634 98404 Hans Havermann 07/2020 9970 (47*10^98386+241)/9 98387 Robert Price 06/2022 9971 7^116416+46 98383 Lelio R Paula 08/2016 9972 7^116407-24 98376 Lelio R Paula 07/2016 9973 439^37228+37228^439 98374 Norbert Schneider 08/2018 9974 2^326782-1860671 98372 Enzo Doria 03/2016 9975 17^79948+58 98372 Lelio R Paula 08/2016 9976 22499^22602-22602^22499 98368 Norbert Schneider 08/2020 9977 3^206143-98 98356 Lelio R Paula 08/2016 9978 8*5^140705+7 98350 Lelio R Paula 11/2014 9979 (2^326632+1662)/2 98326 Stefano Morozzi 09/2020 9980 (638^35053-1)/637 98315 Serge Batalov 06/2022 9981 2^326585+11 98312 Lelio R Paula 12/2012 9982 2^326582-459161 98311 Enzo Doria 05/2015 9983 (1266^31687-1)/1265 98304 Serge Batalov 06/2022 9985 (2^326548+9)/5 98301 Lelio R Paula 10/2013 9984 (2^326549+18)/10 98301 Stefano Morozzi 03/2020 9986 2^326538+71659 98298 Enzo Doria 04/2016 9987 (2^326520+2082)/2 98293 Stefano Morozzi 09/2020 9988 (2^326521+1002)/2 98293 Stefano Morozzi 09/2020 9989 15^83575-58 98292 Lelio R Paula 08/2016 9990 10^98288+3 98289 Robert Price 03/2011 9991 10^98288-117017 98288 Patrick De Geest 11/2011 9992 (44*10^98284-719)/9 98285 Robert Price 12/2017 9993 (5985^26021-1)/5984 98280 Serge Batalov 06/2022 9994 23466^15419+15419^23466 98277 Hans Havermann 02/2020 9995 2^326421-2797573 98263 Enzo Doria 04/2016 9996 2^326401+16095 98257 Lelio R Paula 07/2016 9997 (6494^25771-1)/6493 98249 Serge Batalov 06/2022 9998 7^116240-116240^7 98235 Norbert Schneider 05/2017 9999 17^79826-78 98222 Lelio R Paula 08/2016 10000 2^326268-809 98217 Yves Minet 04/2011

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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